EFFECT OF STRESS ON THE MAGNETIC PROPERTIESOF STEEL WIRE
By R. L. Sanford
ABSTRACT
The work here described is a part of a more extended investigation on nondestruc-
tive methods of testing wire rope. Data are given in terms of magnetic relucti\nty
showing the effect of stress on the magnetic properties. It is found that the reluc-
tivity, which is a linear function of the magnetizing force for pure homogeneousmaterials, no longer shows such a linear relationship when tension is applied to the
wire. It is shown how two components of the material differing only as regards
stress condition and each following the linear relationship can be combined to give
the results found by experiment. This metliod of analysis seems to be capable of
further development and extension into other fields of magnetic analysis.
CONTENTSPage
I. Introduction 68i
II. The reluctivity relationship 683
III. Observations and results 684
IV. Theory 686
V. Analysis of experimental data 689
VI. Siunmary 694
I. INTRODUCTION
It has long been knowra that mechanical stress has a marked
influence on the magnetic properties of iron and steel. Manyinvestigations of this effect have been carried out and its general
nature is very well understood. It is doubtful, however, whether
the disturbing influence of this factor in the attempt to establish
definite correlations between magnetic properties and other
physical properties has hitherto been sufficiently well recognized.
Although the disturbing effect of stress on the magnetic properties
is most marked for moderate values of magnetizing force, it is
within this range that a majority of the researches on corre-
lation of magnetic properties with effects other than stress have
been made. Figure i illustrates the effect of a relatively moderate
degree of tension on the magnetic permeability of steel wire, such
as used in the manufacture of wire rope.^
1 The •work here described is part of a more comprehensive investigation •n nondestructive methodsfor testing wire rope. In view of the difficulty in the interpretation of results encountered in previous
investigations of a similar nature, a study is first being made of the effects on the magnetic properties dTarious causes of deterioration in wire rope.
681
682 Scientific Papers of the Bureau of Standards [Vd. iQ
In view of the fact that the permeability at a given value of
magnetizing force may be nearly doubled by the application of a
small amount of stress, it is not difficult to understand that the
effect of various other factors, such as chemical segregations or
changes in metallographic structure, on the magnetic properties
may be entirely masked by residual stress effects resulting from
mechanical work or heat treatment during the process of manu-facture. It is obvious, therefore, that, in any satisfactory method
zoooo
B
ISOOO
too00
sooo
2SS0O /iis.per^$fJ^^,^
/f^0hii4
•
SOO
zso
25 50 75
Magnetizing Force (H)
too
Fig. I.
—
Effect of mechanical stress on the magnetic properties of steel
of magnetic exploration for the detection of flaws and imperfec-
tions, either the indications of the instruments must be inde-
pendent of the effect of stress or a method must be available for
evaluating this effect so that it can be eliminated from the results.
Up to the present time no magnetic method for the detection of
flaws and imperfections has been described, the results of which
are unambiguous and free from the difficulties just mentioned.
The object of the present investigation was to establish, if
possible, a quantitative relationship between stress and magnetic
sanford] Efjcct of Stvess Oil Magnetic Properties 683
properties in the hope of discovering some method by which the
effects of stress can be properly taken into account. Although
but a single special case has been covered, a method of analysis
has been worked out, which seems to warrant further study and
application in other cases and consequently is described at this
time.
II. THE RELUCTIVITY RELATIONSHIP
Although the effect of stress is greatest at moderate values of
magnetizing force, it is not easy to make a quantitative study of
its magnitude in this range because there is no adequate method
of expressing the magnetic properties in terms of a simple mathe-
matical formula. For this reason, observations were made at
high magnetizing forces in the range covered by Kennelly's law.^
This law, which has been referred to as the reluctivity relationship
shows a linear relationship between metallic reluctivity and
magnetizing force and is expressed as follows
:
p = a + (3H
in which
p = metallic reluctivity( p~tT )
//--magnetizing force
a and /3 = constants characteristic of the material.
Above a certain minimum value of magnetizing force this law
has been found to hold for pure homogeneous materials. It is
to be noted that metallic induction (B-H) and metallic reluctivity
( -^-7^ ] must always be used in the expression of this relation
which is shown graphically in Figure 2.
/5 is the slope of the reluctivity line and its reciprocal can be
shown to be equal to the saturation value of the metallic induction.
Q= (^-//)max
a is the intercept of the line on the reluctivity axis and, since it
indicates the rate at which magnetic saturation is approached,
has been termed the "coefficient of magnetic hardness." a and
/3, then, may be properly considered as magnetic constants for
pure, homogeneous material.
For impure or inhomogeneous materials the reluctivity graph
departs from a straight line by an amount depending upon the
* Kennelly, Am, Inst. Elec Eng. Trans., 8, p, 485; 1891.
684 Scientific Papers of the Bureau of Standards [Vol.19
degree of impurity or inhomogeneity. This departure from a
straight line has been experimentally investigated by Ball,^ whodemonstrated that the departure was due to the presence of twoor more magnetically different components. Ball further con-
cluded that the reluctivity line resulting from two or more different
constituents could be represented as a number of straight portions,
each having a definite value of a. and jS. This conclusion is not
verified by the results of the present investigation, and will be
discussed in more detail later.
In view of the simple nature of the mathematical expression and
of the other facts just referred to, it appeared that the most
^
Q:
^^
^
u-^.^
2C)o **cyo €i70 GtTO tO-OC
Fig.
Ma^n&tiz'inj Force (ti)
-Magnetic reluctivity relationship
promising and logical approach to the problem in hand was byway of the reluctivity relationship which has already been found
useful in the study of the effect of heat treatment.*
III. OBSERVATIONS AND RESULTS
In order to study the magnetic properties of steel wire in the
light of the reluctivity relationship it was necessary to provide for
the application of magnetizing forces up to i,ooo gilberts per
centimeter. For this purpose a special solenoid 50 cm long waswound on a fiber form. The winding consisted of 10 layers of No.
1 7 silk-enamel wire which would carry 10 amperes for a short time
without undue heating. The concentration of the winding was
such that the .magnetizing force was approximately 100 times the
current in amperes. The ordinary ballistic method was used,-
the test coils of 100 turns each being wound directly on the wire.
3 Ball, Joui-. Frank, Inst., 181, p. 459; 1916.
* Nusbaum, Cheney, and Scott, B. S. Sci. Paper, No. 404; 1920.
Sanford] Effect of Stress on Magnetic Properties 685
Since the wire was only 2.54 mm (o.i inch) in diameter the dimen-
sional ratio was over 200 so that the demagnetizing factor was so
small as to be negligible. The balHstic galvanometer used had
a large external resistance for critical damping and sufficient sensi-
tivity so that it could be used in a heavily overdamped condition,
thus giving practically fluxmeter performance. Calibration was
by means of a standard mutual inductance whose secondary was
kept always in the galvanometer circuit.
The wire under test was placed in a Scott horizontal testing
machine of 2,000 pounds capacity with the magnetizing solenoid
surrounding it, and normal induction data obtained for various
values of applied tension. The material tested consisted of
samples of four grades of steel wire, commonly used in the manu-
facture of wire rope, o.i inch in diameter.^ In view of the fact
that the results were of a similar nature for all of the grades of
wire tested, and, also, that the primary object of this paper is to
describe a method of analysis of the results rather than to present
data for various kinds of material, the results reported are only
those obtained for the highest grade known as Monitor, which
has an ultimate strength as given by the manufacturers of from
240,000 to 260,000 lbs./in.2
TABLE 1.—Values of Reluctivity f^g^;;;^ j
for Various Loads for Monitor Steel
Wire
[Tension in pounds per square inch]
102,000
100200300400
500600700800
° 25,500 38,250 51,000 63,750 76,500 89,250
1
0.00634 0.00628 0.00631 0.00630 0.00631 0.00633 0.00637. 01105 .01106 .01111 .01115 .01122 .01128 . 01136. 01574 .01582 .01586 . 01592 .01598 .01609 .01622.02040 .02050 .02058 .02064 .02074 .02084 .02095
.02513 . 02522 .02530 .02538 .02546 .02554 .02568
.02981 .02994 . 02997 .03010 .03020 .03024 . 03038
.03444 . 03461 .03461 .03478 .03481 .03496 .03501
.03925 .03938 .03940 .03944 .03957 .03964 .03975
0.00640.01144.01631. 02110
.02580
. 03050
. 03513
. 03982
In Table i are given the values of metallic reluctivity f „ ^.J
calculated from the observed normal induction data for values
of tension up to 102,000 Ibs./in.^ Values are not given for mag-netizing forces below 100 as the linear relationship does not hold
for the lower part of the curve. The effect of stress is to cause
a departiu-e from the linear relationship, the departure becoming
« This wire was kindly furnished by the American Steel & Wire Co.
686 Scientific Papers of the Bureau of Standards [Vol. 19
greater as the tension is increased. This deviation ^ is shown
in Figure 3, in which is shown the difference between p and
^H (A = p — pH). The curves here given also demonstrate the
fact, aheady mentioned, that the reluctivity curve for inhomo-
geneous material can not be considered to be made up of a numberof straight portions with sharp breaks, but that it is a continuous
curve. If there were really a sharp break this A curve would
rise to a sharp maximum, after which the values of A would de-
crease. Several reluctivity curves taken from the results of other
investigations have been examined by this method, and in none
of them is a sharp break to be observed.
IV. THEORY
For purposes of discussion and analysis of the results let us
make some assumptions which appear to be valid in this case and
see if the observed data bear out the resulting theory.
25
20
15
X --3^:^11.~~~-76S00 lbs. perofw.
i,37S0 ' " -
M^^E-——
—
'382S0 •• •• «
£3<S00
^'P fiH
250 500 750
Magnetizing Force (H)
Fig. 3.
—
Deviation from a straight line, parallel to the asymptote but passing through
the origin, of the reluctivity curves for various degrees of tension
(i) Since the magnetic inhomogeneity causing the departure of
the reluctivity relationship from the linear is caused by, and
increases with, the degree of tension, the material must be madeup of a number of components differing only in their condition as
regards stress.
(2) This inhomogeneous condition as regards stress must have
been present in the wire before the application of an external
load, otherwise the reluctivity line would be straight for all values
6 Curves ot p against H are not given since the departure from the linear, though real, is so small that it
can not be shown satisfactorily on a small scale.
sanfordi Effect of Stress on Magnetic Properties 687
of load below the proportional limit. The reason that the lack
of homogeneity is not noticeable at no load is probably that the
proportion of material differing from the rest in stress condition
is either very small or the degree of difference is slight.
(3) Since -^ represents the satm-ation value of magnetization,
which is proportional to the number of elementary magnets per
unit volume, it seems reasonable to assume that this number is
not changed by stress, and consequently that jS is the same for
all the components.
(4) Since the distribution of stress is^ probably the result of the
drawing operation during the process of manufacture of the wire,
it may be assumed that the outside portion is in a state of longi-
tudinal tension balanced by compression in the inner part.
(5) If the stresses are mainly longitudinal then the compo-
nents differing in magnetic properties are in parallel.
(6) For stresses below the proportional limit there are only
two kinds of material, that in tension and that in compression.
Let us assume two components whose magnetic properties can
be represented in terms of reluctivity as
and (i)
p2=a2+^H
If A I and A 2 are the respective proportions of the components
and they are in parallel, the resultant reluctivity is
^^A^ptrk^, ^^^
Substituting the values of Pi and pg from equations (i) we have
a,a2 + {a,+a2)pH + {^H)'
If we call
and
A^a^+A^a^+^H
C2 = «! + ttj
(3)
C,=Aia2+A2ai
equation (3) reduces to the form
8537°—24-
c,+c^H+(my f.
688 Scientific Papers of the Bureau of Standards Woi.iq
which is the equation of an hyperbola whose asymptote is
or
Pa=ni +^Hwhere
tw = C2 — C3
Substituting m + C^ for C2 in equation (4) we find
c,+{m+c,)m+(my
If we take 5 as the amount that the reluctivity deviates from its
asymptote
S=^ + ^//-.=§^' (6)
which is the equation of a straight line from which, if the values
of m and p were known, Cj, Cj, and C3 could be evaluated. Thenfrom the values of Ci, C2, and C3 the values of a^, a^, A^ and A^ can
be found from the following relationships
:
«1 + <^2 =Qa:i-Q:2 = VQ-4Q
^ ^^LZS(8)
A2 = i-Ai
In the present work the value of ^ has been taken as the slope
of the reluctivity line for no load. It is probable that, if the
observations could be made with greater precision, tlie departure
SoHfora] Effect of Stress on Magnetic Properties 689
from a straight line could be noted. With the degree of precision
obtainable, however, the deviation appears to be less than the
probable error.
If we take A as the difference between the reluctivity curve
and a line parallel to the asymptote passing through the origin;
that is
then it can be shown that
A \m^ Amp/'^m ^^^
Since A is a variable function of H the resulting graph is not quite
a straight line. The quantity in parenthesis, however, is small
compared with H/A so that the departure from a linear relation
is slight and the reciprocal of its slope can be taken as the value
of m.
Since the values of 5 are small compared with p a small error in
the determination of p can cause a relatively large error in the
value of 8. It is difl&cult, therefore, to obtain satisfactory curves
of 1/5 against H. In order to overcome this difficulty an addi-
tional relationship was used
' mCs — Cj mCs — Ci
By plotting A/5 against H it is possible to test the validity of the
assumed law and to determine the values of the various constants.
If it is found by plotting the various functions indicated above
against H that straight lines result, we may conclude that, for
a first approximation at least, the material may be considered
to have two components, one of which is in tension and the other
in compression having the respective magnetic properties rep-
resented by equations (i) and having the corresponding propor-
tions represented by A^ and A^ as calculated by means of the
equations given above.
V. ANALYSIS OF EXPERIMENTAL DATA
TT
In Figure 4 are shown the results of plotting values of — against
H. For loads up to and including 76,500 Ibs./in.^ the lines are
690 Scientific Papers of the Bureau of Standards [Vd. iQ
straight within the limits of experimental error, which indicates
that our assumptions are valid within this range. For values
above 76,500 Ibs./in.^ the lines show a distinct curvature. This
may be explained by considering that above the proportional
limit some of the material has failed mechanically and no longer
carries any of the load. It does, however, continue to carry
magnetic flux and, therefore, constitutes a third magnetic com-
250 500
Magnetizing Force (H)
Fig. -Relationship of — to magnetizing force for various degrees of tensionA
ponent. This being the case, the two-component laws can no
longer be expected to hold. We conclude, therefore, that the
proportional limit has been passed for loads above 76,500 Ibs./in.^J
Figure 5 shows the variation of m, the intercept of the asymptote
of the reluctivity curve, with the load. Within the limits of
' Extensometer measurements indicated about i27,ocx)lbs./in.» as the proportional limit, but it is thought
that the magnetic indications are more sensitive.
Sanford] Effect of Stress on Magnetic Properties 691
experimental error this relationship appears to be a linear one.
As before stated the value of ^ was taken as the slope of the
reluctivity line for no load and in this case, is equal to 468 X IO~^
25
zo
15
20000 AOOOO 60000
Tension - lbs. per Cf in.
Fig. 5.
—
Variation of the intercept of the symptoie to the reluctivity linefor various degrees
of tension
In Figure 6 are shown values of A/5 plotted againstH for stresses
below the proportional limit. From these curves the values
given in Table 2 were obtained.
TABLE 2.—Constants 1 Calculated From Reluctivity Data for Monitor SteelWire Under Various Loads
[Tension in pounds per square inch]
25,500 38,250 51,000 63,750 76,500
m 0. 001902.24.0315
6.326.72
4.825.591.13.17.83
0. 002011.13.0275
3.815.63
3.624.85.78.30.70
0. 00211.76.0253
2.965.37
3.264.75.62.36.64
0. 00222.34.02441.454.79
2.574.46.33.46.54
0. 00232a . . 06b .0239C1XIO8 .30C2XIO3 4.40
C3XIO3 2.08aiXlO' . . 4 33aaXlOa .07
53As .47
^=468X10-'
J m determined from the equation H/A= ( —^-—^ )+~
"
a and 6 found from the equation -r=a+bH,
where a=:
a
Ciand 6=
w/3
niCz—C\ " mCz—Ci
Ci=-^OT/S,C3=-r-(l+a) and C¥=m-\-Cz a\, az, Ai and As calculated from equations (8) above.
692 Scientific Papers of the Bureau of Standards [Vd. IQ
The data of Table 2 are shown graphically in Figure 7. The
agreement between the observed values of reluctivity and those
ioo zoo soo ^00 500
Magnetizing Force (H)
Fig. 6.
—
Variation of — uiih magnetizing forcefor -various degrees of tension
calculated from the constants a^, a^, A^ and A2 is shown in
Table 3.
TABLE 3.—Observed and Calculated Values of Reluctivity
[Tension in pounds per square inch]
25,500 38,250 51,000 63,750 76,500
HOb-
servedCalcu-lated
Ob-served
Calcu-lated
Ob-served
Calcu-lated
Ob-served
Calcu-lated
Ob-served
Calcu-lated
100-
.
0. 00628. 01106. 01582. 02050
. 02522
.02994
. 03461
.03938
0.00627.01105
' . 01578.02049
. 02520
. 02991
.03459
.03927
0.00631. 01111.01586. 02058
.02530
. 02997
.03461
.03940
0.00626.01109. 01584. 02057
. 02526
.02995
. 03468
.03937
0.00530.01115. 01592.02064
. 02538
. 03010
.03478
. 03944
0.00630.01116. 01593.02064
. 02537
.03007
. 03476
. 03945
0. 00631. 01122. 01598.02074
. 02546
. 03020
. 03481
.03957
0.00632. 01122. 01601. 02075
. 02546
.03019
.03485
. 03958
0.00633.01128.01609. 02084
.02554
.03024
.03496
.03964
0.00632
200 .01129
300 .01609
400 . 02084
500 . 02556
600 .03026
700 .03495
800 .03965
Sanford] Effect of Stress on Magyietic Properties 693
The difference between the observed and calculated values
of reluctivity is in no case as great as the possible experimental
error.
It is not possible from the data here reported to determine the
functional relationship between a and stress. This question
furnishes a subject for further research. It is apparent that
a decreases with increasing tension or decreasing compression.
It is, of course, realized that there must be a gradual transition
in the material from a state of tension to one of compression, but
it appears that the observations have not sufficient precision to
ZOQOO ^0000 60000
Tension- Jb^.per 6a /n.
Fig. 7.
—
Variation of constants a^ ol^ ^\ ^^^ ^2 '"'*^^ appl led tension
indicate this condition. The values of a. and A must be considered
as approximations, but it is felt that the results represent the
conditions in the main fairly well.
The material under no load is in equilibrium, a small propor-
tion of material under a relatively high degree of tension being
balanced by a large proportion of the material under a corre-
spondingly smaller degree of compression. As tension is applied,
the proportion of the material in tension increases as well as the
relative intensity of the tensile stress as represented by the in-
crease in A^ and the decrease in a^. All of the material has not
been brought into a condition of tension until some has actually
694 Scientific Papers of the Bureau of Standards [Vd. ig
failed, thus constitu'ting an additional magnetic component.
The mathematical method of solving the reluctivity expression
for three components has not been worked out.
It is probable that a further consideration of the phenomenamay lead to a better conception of the effect of stress on mag-
netic properties including the "Villari reversal" and possibly
the phenomena of magnetostriction. It is to be understood that
this method of analysis so far as it has been developed here
applies only to the case of material uniform in magnetic proper-
ties except for the influence of stress and in which the parallel
arrangement can reasonably be expected to hold. It seems pos-
sible, however, that methods might be found of applying the sameprinciples in a more general way. At any rate a field of investi-
gation is opened up which should prove to be of great value in
explaining many of the interrelations between magnetic proper-
ties and other physical properties.
VI. SUMMARY
The results of this investigation may be summed up briefly
as follows:
(i) To the marked influence of mechanical stress on magnetic
properties, especially in the steep part of the magnetization
curve, may be attributed much of the difficulty heretofore experi-
enced in establishing definite laws of correlation between the
magnetic and other physical properties of iron and steel.
(2) In any satisfactory method of magnetic exploration for the
detection of flaws in steel it must be possible to eliminate the
effects of stress either experimentally or by calculation.
(3) When the reluctivity relationship departs from the linear
due to impurities or inhomogeneity the result is not a series of
straight lines with sharp breaks, but a continuous curve.
(4) The reluctivity curve for inhomogeneous material is the
resultant of two or more straight lines which represent the mag-
netic properties of the corresponding components making up the
material.
(5) If there are only two components, in parallel, and differ-
ing only as regards stress conditions, it is possible to calculate
the relative proportions of these components and the straight
lines representing their magnetic properties by the method here
described.
Sanford] Efject of Stvess on Magnetic Properties 695
(6) When the applied stress is beyond the proportional limit
of the material the laws for two components no longer hold.
(7) Within the proportional limit there is approximately a
linear relationship between the applied stress and the intercept
on the p axis of the asymptote to the reluctivity curve.
(8) Values of reluctivity calculated from the constants obtained
by the method of analysis here described agree with the observed
values well within the limits of experimental error.
(9) The data and method of analysis here presented open up
a new method of approach to the problem of the correlation of
magnetic properties with other physical properties which is worthy
of further development and which should yield valuable results
in this field.
In conclusion the author wishes to acknowledge the great
assistance of Dr. Chester Snow in the development of the mathe-
matical theory and to M. F. Fischer, H. J. Hoyert, and J. M.
Barry for the determination of the experimental data and cal-
culation of the results.
Washington, June 22, 1924.
' :• (Mil! riv-*
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